The propagation delay in the timing of a pulsar orbiting a supermassive black hole

  • Eva HackmannEmail author
  • Arnab Dhani
Editor’s Choice (Research Article)


The observation of a pulsar closely orbiting the galactic center supermassive black hole would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravitational field of the black hole. Due to the extreme mass ratio of the pulsar and the supermassive back hole we use the test particle limit to derive an exact analytical formula for the propagation delay in a Schwarzschild spacetime. We then compare this result to the propagation delays derived in the usually employed post-Newtonian approximation, in particular to the Shapiro delay up to the second post-Newtonian order. For edge-on orbits we also consider modifications of the Shapiro delay which take the lensing effects into account. Our results are then used to assess the accuracy of the different orders of the post-Newtonian approximation of the propagation delay. This comparison indicates that for (nearly) edge-on orbits the new exact delay formula should be used.


Black holes Light propagation Pulsar timing 



The authors thank the research training group GRK 1620 ”Models of Gravity”, funded by the German Research Foundation (DFG), for support. E.H. gratefully acknowledges support from the DFG funded collaborative research center SFB 1128 ”Relativistic geodesy with quantum sensors (geo-Q)”. A.D. is thankful to University of Bremen for its hospitality and support where this work was conceptualized. We thank D. Schwarz and J. Verbiest for fruitful discussions.


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Copyright information

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Authors and Affiliations

  1. 1.Center of Applied Space Technology and Microgravity (ZARM)University of BremenBremenGermany
  2. 2.Faculty of PhysicsUniversity of BielefeldBielefeldGermany
  3. 3.Institute for Gravitation and the CosmosThe Pennsylvania State University, University ParkPennsylvaniaUSA
  4. 4.Department of PhysicsPennsylvania State UniversityUniversity ParkUSA
  5. 5.Department of PhysicsIndian Institute of Technology RoorkeeRoorkeeIndia

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